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Leetcode Problem 813. Largest Sum of Averages

813. Largest Sum of Averages

Leetcode Solutions

Dynamic Programming Approach for Partitioning Array for Maximum Sum of Averages

  1. Calculate prefix sums for the input array nums to allow constant time average calculation.
  2. Initialize a 2D array dp where dp[i][k] will hold the maximum score for partitioning nums[i:] into k subarrays.
  3. Populate the dp array starting from the smallest subproblems (largest i and smallest k) and build up to the solution.
  4. For each i and k, consider all possible partitions by iterating over j where i < j <= N, and calculate the score for each partition as the sum of the average of nums[i:j] and dp[j][k-1].
  5. The answer is dp[0][k], which represents the maximum score for partitioning the entire array into at most k subarrays.
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